where \(P_{k-1}(T)\)  is certain polynomial of degree \(k-1\)  (see [1]}). The mean square of \(\Delta _k(x)\)  has been computed by Cramér [2]} for \(k=2\)  and by Tong [3]} for \(k\ge 3\)  (assuming the Riemann Hypothesis for \(k\ge 4\) ) and was found to be
\(\frac{1}{X}\int _{X}^{2X} \Delta _k(x)^2 dx \sim c_kX^{1-\frac{1}{k}},\) 
